How do I solve non manifold errors with this relatively simple shape?
I would stick with the extrusion method, personally, but you do have to be aware of doubled edges or faces, depending on how you extruded it.  I would look at it in Wireframe mode to see if you have anything like this:

The red arrow is showing a doubled-up face inside the object, so you'd want to delete any of those.
The blue arrow is showing an edge that is ACTUALLY a face (with zero height).
Have you tried simply doing a Merge By Distance to clean up any vertices that are doubled up, or just realllly close to each other?
Also, silly question, but have you tried clicking that &quot;Make Manifold&quot; button there on the right side?
If nothing helps, you could upload the blend file.  If you don't want to upload it because there are other objects in the scene, you could save a copy and delete everything else.